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Escaping a Neighborhood Along a Prescribed Sequence in Lie Groups and Banach Algebras

Part of: General theory of linear operators Lie groups

Published online by Cambridge University Press:  02 October 2019

Catalin Badea ,
Vincent Devinck  and
Sophie Grivaux
Catalin Badea
Affiliation:
CNRS, Univ. Lille, UMR 8524 - Laboratoire Paul Painlevé, France Email: catalin.badea@univ-lille.frsophie.grivaux@univ-lille.frURL: http://math.univ-lille1.fr/∼badea/http://math.univ-lille1.fr/∼grivaux/
Vincent Devinck
Affiliation:
Univ. d’Artois, Laboratoire de Mathématiques de Lens, FR2037 CNRS, France Email: devinck@math.cnrs.fr
Sophie Grivaux
Affiliation:
CNRS, Univ. Lille, UMR 8524 - Laboratoire Paul Painlevé, France Email: catalin.badea@univ-lille.frsophie.grivaux@univ-lille.frURL: http://math.univ-lille1.fr/∼badea/http://math.univ-lille1.fr/∼grivaux/
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Abstract

It is shown that Jamison sequences, introduced in 2007 by Badea and Grivaux, arise naturally in the study of topological groups with no small subgroups, of Banach or normed algebra elements whose powers are close to identity along subsequences, and in characterizations of (self-adjoint) positive operators by the accretiveness of some of their powers. The common core of these results is a description of those sequences for which non-identity elements in Lie groups or normed algebras escape an arbitrary small neighborhood of the identity in a number of steps belonging to the given sequence. Several spectral characterizations of Jamison sequences are given, and other related results are proved.

Keywords

Jamison sequencepoint spectrumiterateaccretive operatorBanach algebraLie groupgroup with no small subgroupsminimal metric

MSC classification

Primary: 47A10: Spectrum, resolvent
Secondary: 47A12: Numerical range, numerical radius 47A60: Functional calculus 22E15: General properties and structure of real Lie groups
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 3 , September 2020 , pp. 484 - 505
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Copyright
© Canadian Mathematical Society 2019

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Footnotes

This work was supported in part by the project FRONT of the French National Research Agency (grant ANR-17-CE40-0021) and by the Labex CEMPI (ANR-11-LABX-0007-01).

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